Beefy Boxes and Bandwidth Generously Provided by pair Networks
The stupid question is the question not asked

Re: Help with Matrix math!

by rg0now (Chaplain)
on Dec 17, 2007 at 19:04 UTC ( #657486=note: print w/replies, xml ) Need Help??

in reply to Help with Matrix math!

What you are trying to solve is a nonlinearly constrained nonlinear (actually, quadratic) mathematical program. This is a tough one, I can tell you...

However, all is not lost, because you might be able to simplify your problem into something actually soluble.

First: are you absolutely sure that you want to optimize over the boundary of the unit ball (this is what the constraint x'x=1 seems to impose)? Isn't it enough to only assure that x is constrained into a sane region, like e.g., the n-dimensional unit box? If it is, you get a quadratic program:

max_x (x' D x) s.t. -1 <= x_i <= 1 \forall i=1..n
See more on quadratic programs here: Quadratic programming.

Second: all depends on whether or not your D is negative definite or not (all eigenvalues are negative). If not, you are out of luck: the problem is (at least) NP hard. If, on the other hand, D is nicely negative definite, then the objective function is concave and the uniqueness of the optimal solution is guaranteed. In this case, you could use a commercial quadratic solver, like CPLEX, or, after suitable linearization, a linear program solver. too. E.g., this one Math::GLPK has a nice Perl interface (believe me it's nice: I wrote it!...:-).

Log In?

What's my password?
Create A New User
Node Status?
node history
Node Type: note [id://657486]
and all is quiet...

How do I use this? | Other CB clients
Other Users?
Others chanting in the Monastery: (2)
As of 2017-07-21 05:06 GMT
Find Nodes?
    Voting Booth?
    I came, I saw, I ...

    Results (318 votes). Check out past polls.